New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation
We study weak type interpolation for ultrasymmetric spaces L?,E i.e., having the norm ??(t)f*(t)?E˜, where ?(t) is any quasiconcave function and E˜ is arbitrary rearrangement-invariant space with respect to the measure dt/t. When spaces L?,E are not “too close” to the endpoint spaces of interpolatio...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2006/242615 |
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| author | Evgeniy Pustylnik Teresa Signes |
| author_facet | Evgeniy Pustylnik Teresa Signes |
| author_sort | Evgeniy Pustylnik |
| collection | DOAJ |
| description | We study weak type interpolation for ultrasymmetric spaces L?,E i.e., having the norm ??(t)f*(t)?E˜, where ?(t) is any quasiconcave function and E˜ is arbitrary rearrangement-invariant space with respect to the measure dt/t. When spaces L?,E are not “too close” to the endpoint spaces of interpolation (in the sense of Boyd), the optimal interpolation theorem was stated in [13]. The case of “too close” spaces was studied in [15] with results which are optimal, but only among ultrasymmetric spaces. In this paper we find better interpolation results, involving new types of rearrangement-invariant spaces, A?,b,E and B?,b,E, which are described and investigated in detail. |
| format | Article |
| id | doaj-art-64399f58726b4105b8f0e8c2c5023d8f |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-64399f58726b4105b8f0e8c2c5023d8f2025-02-03T05:59:05ZengWileyJournal of Function Spaces and Applications0972-68022006-01-014327530410.1155/2006/242615New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolationEvgeniy Pustylnik0Teresa Signes1Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, IsraelDepartamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo (Murcia), SpainWe study weak type interpolation for ultrasymmetric spaces L?,E i.e., having the norm ??(t)f*(t)?E˜, where ?(t) is any quasiconcave function and E˜ is arbitrary rearrangement-invariant space with respect to the measure dt/t. When spaces L?,E are not “too close” to the endpoint spaces of interpolation (in the sense of Boyd), the optimal interpolation theorem was stated in [13]. The case of “too close” spaces was studied in [15] with results which are optimal, but only among ultrasymmetric spaces. In this paper we find better interpolation results, involving new types of rearrangement-invariant spaces, A?,b,E and B?,b,E, which are described and investigated in detail.http://dx.doi.org/10.1155/2006/242615 |
| spellingShingle | Evgeniy Pustylnik Teresa Signes New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation Journal of Function Spaces and Applications |
| title | New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation |
| title_full | New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation |
| title_fullStr | New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation |
| title_full_unstemmed | New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation |
| title_short | New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation |
| title_sort | new classes of rearrangement invariant spaces appearing in extreme cases of weak interpolation |
| url | http://dx.doi.org/10.1155/2006/242615 |
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